On Thursday, February 14, 2013 6:05:23 PM UTC, Jussi Piitulainen wrote:> pepstein5@gmail.com writes:...> > > > > > David Ullrich is wrong. "X to Y" means that the probability of> > > winning is (X + Y)/Y.> > > > Which you later corrected to the reciprocal X/(X + Y); probabilities> > need to be between 0 and 1. But then it seems to me that Ullrich says> > the same, and that's also what I meant.>

No, the reciprocal of (X + Y)/ Y is Y/(X + Y) which is what I should have said.Ullrich wrongly said X/(X + Y).> > My expression above is still off. I appreciate the input. Thanks.> > > > > "X to Y against" means that the probability of winning is (X + Y)/Y> > > and X is larger than Y.> > > > The probability should be X/(X + Y). Also, X _smaller_ than Y, so that> > the odds are against one who bets on the outcome associated with X,> > right?> No, Y/(X + Y) is correct.

> > "X to Y on" means that the probability of winning is (X + Y)/Y and X> > > is less than Y.> > > > Similarly, X/(X + Y) but now X _larger_ than Y, right?> > > > > In this context "on" and "against" are redundant. However, these> > > words enable useful abbreviations as follows. "Twos on" means " 1> > > to 2 " "Twos against" means "2 to 1". You can also write a slash> > > "/" instead of the word "to".> > > > Odds are treated as the numerical fractions suggested by the notation> > when one calculates things like log odds. Would X/Y be read "X to Y"> > in that context?> > > > Some day I'll dig up the books where I've seen these used. Mainly a> > collection of I.J. Good and the posthumous E.T. Jaynes volume.